Integral geometry of the action of ST(3) on the space E3

• Autores: Ana Berenice Guerrero Gutiérrez
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 26, Nº. 1-4, 1992, 180 págs.
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • ABSTRACT. Some aspects of the integral geometry of the action on E3 of the group ST(3) of upper triangular 3x3-matrices of determinant one are studied Measurability for sets of linear surfaces is considered and it is shown that invariant measures do exist for sets of points or planes but not for sets of lines. Measurability for sets of couples point-line and point-plane is also discussed, and the existence of invariant measures is established in both cases. Explicit geometric formulae are given for the measures whenever they exist

• Referencias bibliográficas
  • GUERRERO, B., (1989), Geometría integral de los grupos triangulares ST(n + 1) y STi(n + 1) en el espacio proyectivo Pn, Rev. Col....
  • SANTALO, L. A., 1976, Integral geometry and geometric probability, Addison Wesley, Reading, Mass.
  • STOKA, M. S., (1962), Geometrie integrale dans Vespace E3, Rev Mat. Fis. Univ. Tucuman.
  • STOKA, M. S., 1968, Geometrie integrale, Gauthier-Villars, Paris.